A lower bound on the 2-adic complexity of the modified Jacobi sequence

作者：Sun, Yuhua^*; Wang, Qiang; Yan, Tongjiang

来源：Cryptography and Communications, 2019, 11(2): 337-349.

DOI：10.1007/s12095-018-0300-y

• Gauss period
• Generalized cyclotomic class
• Modified Jacobi sequence
• 2-adic complexity

Let p, q be distinct primes satisfying gcd(p -1, q -1) = d and let Di, i = 0, 1, center dot center dot center dot, d -1, be Whiteman's generalized cyclotomic classes with Z * pq =. d-1 i= 0 Di. In this paper, we give the values of Gauss periods based on the generalized cyclotomic sets D * 0 =. d 2 -1 i= 0 D2i and D * 1 =. d 2 -1 i= 0 D2i+ 1. As an application, we determine a lower bound on the 2-adic complexity of the modified Jacobi sequence. Our result shows that the 2-adic complexity of the modified Jacobi sequence is at least pq -p-q -1 with period N = pq. This indicates that the 2- adic complexity of the modified Jacobi sequence is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).

• 出版日期2019-3
• 单位中国石油大学（北京）; 山东省科学院; 莆田学院